问题 解答题

一队旅客乘坐汽车,要求每辆汽车的乘客人数相等,起初每辆汽车乘22人,结果剩下一人未上车;如果有一辆汽车空车开走,那么所有旅客正好能平均分乘到其它各车上.已知每辆汽车最多只能容纳32人,求起初有多少辆汽车?有多少旅客?

答案

设起初有汽车m辆,开走一辆空车后,平均每辆车所乘旅客为n人;

由于m≥2,n≤32,依题意有22m+1=n(m-1).

所以n=

22m+1
m-1
=22+
23
m-1

因为n为自然数,所以

23
m-1
为整数,因此:m-1=1,或m-1=23,即 m=2或m=24.

当 m=2时,n=45(不合题意,舍去);

当m=24时,n=23(符合题意).

所以旅客人数为:n(m-1)=23×(24-1)=529(人).

答:起初有汽车24辆,有乘客529人.

选择题
阅读理解

第三部分:阅读理解(共20小题,每小题2分,满分40分)

阅读下列短文,从每题所给的四个选项(A、B、C和D)中,选出最佳选项,并在答题卡上将该项涂黑。

Sometimes you make a wish, but when it comes. you decide you don’t want it. That’s what happened with Micky’s “birthday wish”.

Our family tradition is that you make a wish before you blow out the birthday candle.  After he blew out the candle. Micky told us that his wish was to win a prize in the Pine Ridge-match. We quickly told Micky, “If you tell people your wish. your wish won’t come true.” So we lit the candle again, and he made another wish.

Micky and Paul were both supposed to start playing at 5:30.

When Micky reported to the check-in table, the game organizers told him his opponent (对手) had phoned and said he was coming late. The officials told Micky he could choose not to play and be declared the victor of the first round of competition.

But Micky said he didn’t want to win by not playing. He wanted the experience of playing a great player.

Finally, the beast showed up. He was tall, smiling and relaxed. His serve (发球) was like lightning.

Micky had some good returns, but he lost quickly, 6-1, 6-0.

We congratulated Micky on having some good returns and a few great serves. And we noted that he had won the first game.

“I didn’t win that game,” Micky said. “I think he just gave it to me at the beginning because he arrived late.”      

“It was a birthday present.” I said, smiling.

“No, I refused my birthday present,” Micky said. In his eyes, his “birthday present” had been the chance to win by his opponent’s being late.

Micky ended up winning the “consolation prize(鼓励奖)” a small prize that we didn’t know existed until Micky earned it by being undefeated in the consolation bracket (档次).

We’ll’ never know what Micky’s second wish was - the wish he didn’t share with us.

It seems to me that no matter how many birthdays you celebrate, as long as you enjoy challenges, you will never be “old”.

56. What kind of person is Micky?

A. A person who always gives up.          B. A person who is afraid of challenges.

C. One who enjoys challenges.               D. One who is selfish.

57. Why did Micky lose the match?

A. Because he gave up a good chance.           B. Because he let the others know his birthday wish.

C. Because he was proud of himself.       D. Because his opponent played much better than him

58. The prize Micky won was ______.

A. one he had expected                                B. not a well-known one

C. a famous one                                  D. one he thought meaningless

59. It can be inferred from the last paragraph that ______.

A. enjoying challenges is helpful for one to keep “young”

B. one will become old as he celebrates his birthdays

C. one will stay young by continuously celebrating his birthdays

D. challenges can make one never get old